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    \$\begingroup\$ AnyDice can compute large binomial distributions just fine, though; you just have to be slightly smart about how to write the code so that it doesn't waste time enumerating too many equivalent rolls. :) \$\endgroup\$ Commented Sep 12, 2022 at 15:42
  • \$\begingroup\$ @IlmariKaronen Yep, I recognize that Anydice is quite powerful, but SE's program halts for small N: one has to have a strong anydice-fu as you to overcome problems like these. I am aware that I usually answer to questions about Anydice with pure mathematical solutions, because I find that even if Anydice is very powerful it makes one lose the deeper insight that a math analysis can provide.. \$\endgroup\$ Commented Sep 12, 2022 at 16:55